Vehicle localization using roadside LiDARs can provide centimeter-level accuracy for cloud-controlled vehicles while simultaneously serving multiple vehicles, enhanc-ing safety and efficiency. While most existing studies rely on repetitive scanning LiDARs, non-repetitive scanning LiDAR offers advantages such as eliminating blind zones and being more cost-effective. However, its application in roadside perception and localization remains limited. To address this, we present a dataset for infrastructure-based vehicle localization, with data collected from both repetitive and non-repetitive scanning LiDARs, in order to benchmark the performance of different LiDAR scanning patterns. The dataset contains 5,445 frames of point clouds across eight vehicle trajectory sequences, with diverse trajectory types. Our experiments establish base-lines for infrastructure-based vehicle localization and compare the performance of these methods using both non-repetitive and repetitive scanning LiDARs. This work offers valuable insights for selecting the most suitable LiDAR scanning pattern for infrastruc-ture-based vehicle localization. Our dataset is a signifi-cant contribution to the scientific community, supporting advancements in infrastructure-based perception and vehicle localization. The dataset and source code are publicly available at: https://github.com/sjtu-cyberc3/BenchRNR.